As far as I know, civilian guns are strictly prohibited on military bases.
Exactly, there is more gun control on a military base then in the civilian world. Unauthorized use of weaponry, even in benign instances, can lead to serious disciplinary actions. The military takes weapons safety VERY seriously.
CNN is talking about M-16s like they're laying around the base like drinking fountains. It's easier to get your hands on a fistful of diamonds, than it is to get your unauthorized hands on an M-16.
Banning guns has little to do with safety. It does provide these sorts of whack jobs with an unarmed target zone.